Germany | Can you solve this ? | Maths Olympiad | (x,y)= ?

Ajouté : 2026-05-30

[00:00:00]Hello. You're welcome to solve this math problem, which is x + y is equal to 24.

[00:00:08]x * y is equal to 44.

[00:00:11]To find the values of x and y's from these two systems of equations.

[00:00:16]Now, in the first step, let's start by letting this as equation one and this as equation two.

[00:00:24]Then, from equation one, which is this here, x + y is equal to 24.

[00:00:33]Into here, we make y the subject, so take x to the right side, then it will be y is equal to 24 minus x.

[00:00:42]Then, let's call this equation three.

[00:00:46]Then, from equation two, where is equation two? It is x * y is equal to 44.

[00:00:55]Into y, we substitute 24 minus x, so it will be x * y is 24 minus x bracket is equal to 44.

[00:01:08]Then here, we multiply x * 24, it is 24 x.

[00:01:13]x * negative x is negative x squared is equal to 44.

[00:01:19]Then here, we start by this here, negative x squared, then plus 24 x.

[00:01:27]Take 44 to this side, so it will be minus 44 is equal to zero.

[00:01:34]Then, into this equation, here negative x squared will make positive, so we divide the whole equation divide by negative one.

[00:01:43]So, negative x squared divide by negative one is positive x squared.

[00:01:49]24 x divide by negative one is minus 24 x.

[00:01:54]Minus 44 divide by negative one, it is plus 44.

[00:02:00]is equal to 0 / -1, it is 0.

[00:02:04]Then into this quadratic equation, we solve by using quadratic formula.

[00:02:09]Whereas coefficients, A is equal to coefficient of x squared, it is 1.

[00:02:15]And B is equal to coefficient of x is -24.

[00:02:21]And C is equal to constant, it is 44.

[00:02:26]Then we'll apply quadratic formula to find the values of x is equal to -b plus or minus square root of b squared -4ac over 2a.

[00:02:42]Then into here, it will be x is equal to -b.

[00:02:47]B is -24.

[00:02:50]Plus or minus square root of b squared.

[00:02:54]It is -24 bracket squared. Then -4 * a, it is 1 * c is 44.

[00:03:04]Then over 2 * a, it is 1.

[00:03:09]Then into here, it will be x is equal to - -24, it is positive 24 plus or minus square root of -24 squared. Negative squared is positive.

[00:03:23]Then 24 squared.

[00:03:26]>> [clears throat] >> 24 * 24. 4 * 4 is 16, goes to 1. 4 * 2 is 8 + 1, it is 9.

[00:03:35]2 * 4 is 8.

[00:03:38]2 * 2 is 4. Then here, 6 7, we add 1 here, it is 5.

[00:03:44]So, 24 squared is 576.

[00:03:49]Then -4 * 4, it is 16. 4 * 4 is 16 + 1, it is 17.

[00:03:56]Then over 2 * 1, it is 2.

[00:04:01]Then into here, it will be x is equal to 24 plus or minus square root of 576 minus 176, it is 0 0. 5 minus 1, it is 4. Then over this two.

[00:04:18]Then into here, it will be x is equal to 24 plus or minus square root of 400, it is 20. Then over two.

[00:04:30]Then into here, it will be x is equal to when it is positive, it is 24 plus 20.

[00:04:37]So here, 24 plus 20 over two.

[00:04:43]This is the first value of x. The second value of x, when it is negative, it is 24 minus 20.

[00:04:53]Then over two.

[00:04:56]So from here, it will be x1 is equal to 24 plus 20, here it is 44 divided by two. 44 divided by two, it is 22. Two.

[00:05:09]Then into here, 24 minus 20, it is four. Then divided by two, four divided by two, it is two. So here, x2 is equal to four divided by two, it is two.

[00:05:23]Then here, we've got x1 x2.

[00:05:27]Then we recall the equation in terms of x, which is y is equals 24 minus x.

[00:05:33]So from y is equal to 24 minus x, this is x1, so here it will be y1 is equal to 24 minus x1 is 22.

[00:05:47]So here, it be y1 is equal to 24 - 22, it is 2.

[00:05:52]So, here x1, this is y1.

[00:05:56]Then, into second solution, we recall this equation here of y is equal to 24 - x.

[00:06:05]So, this is x2. So, here it will be y2 is equal to 24 - x2, it is 2.

[00:06:13]So, here it will be y2 is equal to 24 - 2, it is 22. 2.

[00:06:19]So, this is x2.

[00:06:21]Then, our conclusion x1, {comma} y1 from the first solution x1 is 22, y1 is 2. So, here 22, {comma} 2.

[00:06:36]From the second solution, here x2, {comma} y2 is equal to x2, it is 2. y2 is 22. So, here 2, {comma} 22. 2.

[00:06:50]So, these are all the values of x and y's from this our problem. Whereas, the value of x from the first solution, it is the value of y from the second solution.

[00:07:02]And the value of x from the first value of y from the first solution, it is the value of x from the second solution. So, they interchange the values.

[00:07:12]Now, to check from our problem, which is x + y is equal to 24.

[00:07:20]And we have other equation, x * y is equal to 44.

[00:07:26]So, x + y, we are checking by using the first solution. 22, {comma} 2. So, x is 22 + y is 2. Is it equal to 24?

[00:07:38]Now, 22 + 2 is 44 is equal to Sorry.

[00:07:45]22 plus two is 24 is equal to 24. So, left side and right side are equal.

[00:07:53]Then into here x times y. x c is 22 times y is two. Is it equal to 44?

[00:08:02]Now, 22 times two is 44 is equal to 44.

[00:08:08]Now, left side and right side are equal.

[00:08:11]So, we already check for this first solution.

[00:08:13]Solution, you can check for this second solution.

[00:08:17]Or comment which way did you use or which method you use.

[00:08:23]Because there are many different ways.

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[00:08:35]Bye-bye.